Some continuity properties of quantum R\'enyi divergences
- URL: http://arxiv.org/abs/2209.00646v4
- Date: Tue, 27 Jun 2023 16:02:16 GMT
- Title: Some continuity properties of quantum R\'enyi divergences
- Authors: Mil\'an Mosonyi and Fumio Hiai
- Abstract summary: We prove the equality of two threshold values for the problem of binary quantum channel discrimination with product inputs.
Motivated by this, we give a detailed analysis of the continuity properties of various other quantum (channel) R'enyi divergences, which may be of independent interest.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In the problem of binary quantum channel discrimination with product inputs,
the supremum of all type II error exponents for which the optimal type I errors
go to zero is equal to the Umegaki channel relative entropy, while the infimum
of all type II error exponents for which the optimal type I errors go to one is
equal to the infimum of the sandwiched channel R\'enyi $\alpha$-divergences
over all $\alpha>1$. We prove the equality of these two threshold values (and
therefore the strong converse property for this problem) using a minimax
argument based on a newly established continuity property of the sandwiched
R\'enyi divergences. Motivated by this, we give a detailed analysis of the
continuity properties of various other quantum (channel) R\'enyi divergences,
which may be of independent interest.
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